The value of a function at its maximum or minimum (local or global) is called what?

• A. Extremum (pl. extrema)
• B. Vertex
• C. Concavity
• D. Parabola

Answer: (A)

The value at which a function reaches its highest or lowest point is called an extremum. An extremum is the actual y-value at a point where the function stops increasing and stops decreasing (for a maximum) or stops decreasing and stops increasing (for a minimum). It can be local, meaning the extremum is the highest or lowest in a nearby region, or global, meaning it’s the highest or lowest over the entire domain.

For example, if a function f(x) = -(x-2)^2 + 5, the highest value it attains is 5, which occurs at x = 2. That 5 is the extremum.

The term vertex refers to a specific turning point on a graph of a parabola and isn’t a general label for extreme values of every function. Concavity describes how the graph bends, not the extreme values, and a parabola is just a type of curve, not the value at its extreme.